We now recall some well known notions and
results on the symmetric and alternating parts
of a tensor square (see [1]}, [2]}).
For any finite group \(G\) , we denote by \({\rm Irr}(G)\)  the set of its irreducible (complex) characters, and \(\mbox{$\langle -,- \rangle $}\)  will denote
the usual scalar product on the \(-vector space of class functions on~\) G\(.\)
